Question

How do you use the perfect square trinomial formula to factor `16y^2-8y+1`?

Answer 1

`16y^2-8y+1=(4y-1)(4y-1)`

Explanation:

Here,
`f(y)=16y^2-8y+1`
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To complete perfect square let `M` be the third term,
such that `16y^2-8y +M` is a perfect square.

So,

`color(blue)((i)1^(st) term=16y^2`
`color(blue)((ii)2^(nd)term=-8y`
`color(blue)((iii)3^(rd)term=M`

Formula :
`color(blue)(3^(rd)term=(2^(nd)term)^2/(4xx 1^(st) term)`

`M=(-8y)^2/(4xx16y^2)=(64y^2)/(64y^2)=1`

`i.e. 16y^2-8y+1` is a perfect square.
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So ,

`f(y)=16y^2-8y+1`

`:.f(y)=(4y)^2-2(4y)(1)+(1)^2`

`:.f(y)=(4y-1)^2`